Square Root Calculator
Result
—Calculation Steps
- Enter a non-negative number above.
- Click "Calculate Square Root".
- The result will be displayed here.
Understanding the Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 * 3 = 9. Every positive number has two square roots: a positive one and a negative one. However, in most common mathematical contexts, "the square root" refers to the principal (non-negative) square root, denoted by the radical symbol (√).
Mathematical Notation
If x is a number, its square root y satisfies the equation y² = x. The principal square root is denoted as √x.
Why Calculate Square Roots?
Square roots appear in various fields of mathematics, science, and engineering:
- Geometry: Calculating the length of a side of a square given its area, or finding the hypotenuse of a right-angled triangle using the Pythagorean theorem (a² + b² = c², so c = √(a² + b²)).
- Statistics: Used in calculating standard deviation, a measure of data dispersion.
- Physics: Appears in formulas related to energy, motion, and waves.
- Algebra: Solving quadratic equations and simplifying radical expressions.
How This Calculator Works
This calculator uses JavaScript's built-in `Math.sqrt()` function to compute the square root of the number you provide. This function is highly optimized and accurate. The steps displayed below the result illustrate the process:
- Input: You provide a non-negative number into the input field.
- Validation: The calculator checks if the input is a valid non-negative number.
- Calculation: The `Math.sqrt()` function is applied to the input number.
- Output: The principal square root is displayed, along with a confirmation of the steps taken.
Example Calculation
Let's say you want to find the square root of 144.
1. You enter 144 into the calculator.
2. You click "Calculate Square Root".
3. The calculator computes √144.
4. The result displayed will be 12, because 12 * 12 = 144.
Negative numbers do not have real square roots; attempting to calculate the square root of a negative number typically results in an imaginary number or an error in basic calculators.